Theorems · Theorem · measure theory

MeasureTheory.IsFundamentalDomain.quotientMeasureEqMeasurePreimage_of_zero

∀ {G : Type u_1} {α : Type u_3} [inst : Group G] [inst_1 : MulAction G α] [inst_2 : MeasurableSpace α]
  {ν : MeasureTheory.Measure α} [MeasureTheory.SMulInvariantMeasure G α ν] [Countable G] [MeasurableConstSMul G α]
  {s : Set α}, MeasureTheory.IsFundamentalDomain G s ν → ν s = 0 → MeasureTheory.QuotientMeasureEqMeasurePreimage ν 0

If a fundamental domain has volume 0, then QuotientMeasureEqMeasurePreimage holds.

Defined in

Mathlib.MeasureTheory.Group.FundamentalDomain

Cited by

1 results in Mathlib

Foundations

Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GroupMulActionMeasurableSpaceMeasureTheory.SMulInvariantMeasureCountableMeasurableConstSMul